Probability Class 12 Maths Notes – Formulas & Quick Revision

Class 12 Probability mein conditional probability, Bayes theorem aur probability distributions aate hain. Yahan aapko is chapter ke sabse important formulas aur quick revision points free milte hain — NCERT/CBSE syllabus ke hisaab se, boards aur JEE/NEET dono ke liye.

Important Formulas & Concepts — Probability

• Conditional: P(A|B) = P(A∩B)/P(B)
• Multiplication: P(A∩B) = P(A)·P(B|A)
• Independent: P(A∩B) = P(A)·P(B)
• Total probability: P(A) = ΣP(Eᵢ)·P(A|Eᵢ)
• Bayes: P(Eᵢ|A) = P(Eᵢ)P(A|Eᵢ)/ΣP(Eⱼ)P(A|Eⱼ)
• Random variable: mean E(X) = Σxᵢpᵢ
• Variance = E(X²) − [E(X)]²
• Σpᵢ = 1 (distribution ki condition)

Quick Revision Points

• Bayes theorem ka 6-marker boards mein almost हर saal hai
• Bags/urns/factories wale questions total probability se
• Independent vs mutually exclusive alag concepts hain
• Distribution table mein pehle Σp = 1 se unknown nikalo
• “Given that” dikhe to conditional lagao

FAQ

Bayes ke questions ka format?

Events define karo → prior probabilities → conditional → formula. PDF mein tree-diagram method solved hai.

Distribution ke questions easy hain?

Haan — table banao, mean/variance formulas lagao — 4 marks pakke.

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